Uffizi Gallery, Florence, Op Art, Geometry Online Education

Renoir: Dance at Le Moulin de la Galette (1876) - Tile 2 and Golden Rectangles, Droste Effect, HTML5 Animation for iPad and Tablets

Successive Golden Rectangles dividing a Golden Rectangle into squares (logarithmic spiral known as the golden spiral)

 

Renoir: Bal du moulin de la Galette [Dance at Le Moulin de la Galette], 1876
Artist: Pierre-Auguste Renoir French, 1841 - 1919
Dimensions: H. 131; W. 175 cm
Medium: Oil on canvas
Credit Line: Musée d'Orsay
Style: Impressionism.
This painting is doubtless Renoir's most important work of the mid 1870's and was shown at the Impressionist exhibition in 1877. Though some of his friends appear in the picture, Renoir's main aim was to convey the vivacious and joyful atmosphere of this popular dance garden on the Butte Montmartre. Source: Musée d'Orsay

Golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

Droste Effect
The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration geometrically reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry. Source: Wikipedia, Droste Effect.
 

Renoir: Dance at Le Moulin de la Galette (1876) - Tile 2 and Golden Rectangles, HTML5 Animation for iPad and Nexus